Nonlinear additive autoregressive model-based analysis of short-term heart rate variability

Adaptive and self-learning Bayesian filtering algorithm to statistically characterize and improve signal-to-noise ratio of heart-rate data in wearable devices

The use of wearable sensors to monitor vital signs is increasingly important in assessing individual health. However, their accuracy often falls short of that of dedicated medical devices, limiting their usefulness in a clinical setting. This study introduces a new Bayesian filtering (BF) algorithm that is designed to learn the statistical characteristics of signal and noise, allowing for optimal smoothing. The algorithm is able to adapt to changes in the signal-to-noise ratio (SNR) over time, improving performance through windowed analysis and Bayesian criterion-based smoothing. By evaluating the algorithm on heart-rate (HR) data collected from Garmin Vivoactive 4 smartwatches worn by individuals with amyotrophic lateral sclerosis and multiple sclerosis, it is demonstrated that BF provides superior SNR tracking and smoothing compared with non-adaptive methods. The results show that BF accurately captures SNR variability, reducing the root mean square error from 2.84 bpm to 1.21 bpm and the mean absolute relative error from 3.46% to 1.36%. These findings highlight the potential of BF as a preprocessing tool to enhance signal quality from wearable sensors, particularly in HR data, thereby expanding their applications in clinical and research settings.

Modelling the dynamics of expiratory airflow to describe chronic obstructive pulmonary disease

Chronic obstructive pulmonary disease (COPD) is characterized by expiratory airflow limitation, but current diagnostic criteria only consider flow till the first second and are therefore strongly debated. We aimed to develop a data-based individualized model for flow decline and to explore the relationship between model parameters and COPD presence. A second-order transfer function model was chosen and the model parameters (namely the two poles and the steady state gain (SSG)) from 474 individuals were correlated with COPD presence. The capability of the model to predict disease presence was explored using 5 machine learning classifiers and tenfold cross-validation. Median (95% CI) poles in subjects without disease were 0.9868 (0.9858-0.9878) and 0.9333 (0.9256-0.9395), compared with 0.9929 (0.9925-0.9933) and 0.9082 (0.9004-0.9140) in subjects with COPD (p < 0.001 for both poles). A significant difference was also found when analysing the SSG, being lower in COPD group 3.8 (3.5-4.2) compared with 8.2 (7.8-8.7) in subjects without (p < 0.0001). A combination of all three parameters in a support vector machines corresponded with highest sensitivity of 85%, specificity of 98.1% and accuracy of 88.2% to COPD diagnosis. The forced expiration of COPD can be modelled by a second-order system which parameters identify most COPD cases. Our approach offers an additional tool in case FEV1/FVC ratio-based diagnosis is doubted.

Heart rate variability indices for very short-term (30 beat) analysis. Part 1: survey and toolbox

Heart rate variability (HRV) analysis over very short (<60 s) periods may be useful for monitoring dynamic changes in autonomic nervous system activity where steady-state conditions are not maintained (e.g. during drug administration, or the start or end of exercise). From the 1980s there has been a wealth of HRV indices produced in the quest for better measures of the change in parasympathetic and sympathetic activity. Many of the indices have been sparingly used and have not been investigated for application to short-term use. This study surveyed published methods of HRV analysis searching for indices that could be applied to very short time HRV analysis. The survey included measures of time domain, frequency domain, respiratory sinus arrhythmia, Poincaré plot, and heart rate characteristics. Indices were tested with short segments of archived data to remove those that produced invalid results, or were mathematically equivalent to, but less well known than other indices. The survey identified a comprehensive list of 115 indices that were subsequently coded and screened. Of these, 70 were unique and produced a finite number with 60 s data, so are included in the Toolbox. These indices require validation against physiological data before they can be applied to short-term HRV analysis of cardiac autonomic nervous system activity.

Short-term couplings of the cardiovascular system in pregnant women suffering from pre-eclampsia

Pre-eclampsia (PE), a serious pregnancy-specific disorder, causes significant neonatal and maternal morbidity and mortality. Recent studies showed that cardiovascular variability parameters as well as the baroreflex sensitivity remarkably improve its early diagnosis. For a better understanding of the dynamical changes caused by PE, in this study the coupling between respiration, systolic and diastolic blood pressure, and heart rate is investigated. Thirteen datasets of healthy pregnant women and 10 of subjects suffering from PE are included. Nonlinear additive autoregressive models with external input are used for a model-based coupling analysis following the idea of Granger causality. To overcome the problem of misdetections of standard methods in systems with a dominant driver, a heuristic ensemble approach is used here. A coupling is assumed to be real when existent in more than 80 per cent of the ensemble members, and otherwise denoted as artefacts. As the main result, we found that the coupling structure between heart rate, systolic blood pressure, diastolic blood pressure and respiration for healthy subjects and PE patients is the same and reliable. As a pathological mechanism, however, a significant increased respiratory influence on the diastolic blood pressure could be found for PE patients (p=0.003). Moreover, the nonlinear form of the respiratory influence on the heart rate is significantly different between the two groups (p=0.002). Interestingly, the influence of systolic blood pressure on the heart rate is not selected, which indicates that the baroreflex sensitivity estimation strongly demands the consideration of causal relationships between heart rate, blood pressure and respiration. Finally, our results point to a potential role of respiration for understanding the pathogenesis of PE.

Testing foetal-maternal heart rate synchronization via model-based analyses

The investigation of foetal reaction to internal and external conditions and stimuli is an important tool in the characterization of the developing neural integration of the foetus. An interesting example of this is the study of the interrelationship between the foetal and the maternal heart rate. Recent studies have shown a certain likelihood of occasional heart rate synchronization between mother and foetus. In the case of respiratory-induced heart rate changes, the comparison with maternal surrogates suggests that the evidence for detected synchronization is largely statistical and does not result from physiological interaction. Rather, they simply reflect a stochastic, temporary stability of two independent oscillators with time-variant frequencies. We reanalysed three datasets from that study for a more local consideration. Epochs of assumed synchronization associated with short-term regulation of the foetal heart rate were selected and compared with synchronization resulting from white noise instead of the foetal signal. Using data-driven modelling analysis, it was possible to identify the consistent influence of the heartbeat duration of maternal beats preceding the foetal beats during epochs of synchronization. These maternal beats occurred approximately one maternal respiratory cycle prior to the affected foetal beat. A similar effect could not be found in the epochs without synchronization. Simulations based on the fitted models led to a higher likelihood of synchronization in the data segments with assumed foetal-maternal interaction than in the segment without such assumed interaction. We conclude that the data-driven model-based analysis can be a useful tool for the identification of synchronization.

Modeling the cardiovascular system using a nonlinear additive autoregressive model with exogenous input

The parameters of heart rate variability and blood pressure variability have proved to be useful analytical tools in cardiovascular physics and medicine. Model-based analysis of these variabilities additionally leads to new prognostic information about mechanisms behind regulations in the cardiovascular system. In this paper, we analyze the complex interaction between heart rate, systolic blood pressure, and respiration by nonparametric fitted nonlinear additive autoregressive models with external inputs. Therefore, we consider measurements of healthy persons and patients suffering from obstructive sleep apnea syndrome (OSAS), with and without hypertension. It is shown that the proposed nonlinear models are capable of describing short-term fluctuations in heart rate as well as systolic blood pressure significantly better than similar linear ones, which confirms the assumption of nonlinear controlled heart rate and blood pressure. Furthermore, the comparison of the nonlinear and linear approaches reveals that the heart rate and blood pressure variability in healthy subjects is caused by a higher level of noise as well as nonlinearity than in patients suffering from OSAS. The residue analysis points at a further source of heart rate and blood pressure variability in healthy subjects, in addition to heart rate, systolic blood pressure, and respiration. Comparison of the nonlinear models within and among the different groups of subjects suggests the ability to discriminate the cohorts that could lead to a stratification of hypertension risk in OSAS patients.

Cardiovascular and respiratory dynamics during normal and pathological sleep

Sleep is an active and regulated process with restorative functions for physical and mental conditions. Based on recordings of brain waves and the analysis of characteristic patterns and waveforms it is possible to distinguish wakefulness and five sleep stages. Sleep and the sleep stages modulate autonomous nervous system functions such as body temperature, respiration, blood pressure, and heart rate. These functions consist of a sympathetic tone usually related to activation and to parasympathetic (or vagal) tone usually related to inhibition. Methods of statistical physics are used to analyze heart rate and respiration to detect changes of the autonomous nervous system during sleep. Detrended fluctuation analysis and synchronization analysis and their applications to heart rate and respiration during sleep in healthy subjects and patients with sleep disorders are presented. The observed changes can be used to distinguish sleep stages in healthy subjects as well as to differentiate normal and disturbed sleep on the basis of heart rate and respiration recordings without direct recording of brain waves. Of special interest are the cardiovascular consequences of disturbed sleep because they present a risk factor for cardiovascular disorders such as arterial hypertension, cardiac ischemia, sudden cardiac death, and stroke. New derived variables can help to find indicators for these health risks.